How can I copy or print errors from the console?
As of version 2.77 there is a new built-in 'Reports to Text Block' operator, which basically copies all entries of the Report Console into a newly created text block per execution:





However, saving errors to a text file automatically is might be too complex for a tester to setup (IMO). I'd suggest ask the developer for implementing a debug system. Otherwise you can copy errors and warnings from the terminal output with ease by running Blender via command line.

Linux

1. Run Blender via Command Line

Open a Terminal (Ctl+Alt+T), navigate to the directory where Blender is installed, and run Blender.

cd &lt;blender installation directory&gt;
./blender


This will run Blender with the Terminal window:



Depending on your Window Manager (Gnome, Unity, KDE etc.) you can edit your Launcher or Starter to open up Blender with the command line automatically by setting the 'Terminal flag' to true:

blender.desktop (Ubuntu, Unity)

[Desktop Entry]
Name=Blender
Exec=/opt/blender-2.77a/blender %F
Icon=/opt/blender-2.77a/icons/scalable/apps/blender.svg
MimeType=application/x-blender
StartupNotify=true
Terminal=true
Type=Application
...


2. Copy the Output, Errors or Warnings

Switch to the Terminal, select the text, then RMB and select 'Copy':



Alternatively you can also redirect the output to a text file when using the command line: 

./&lt;blender installation directory&gt;/blender &amp;&gt; ~/mylogfile.txt


Windows

1. Run Blender via Command Prompt

Open the Command Prompt (click Start or hit Win on the keyboard and then type cmd), navigate to the directory where Blender is installed, and then run Blender:

cd c:\&lt;blender installation directory&gt;
blender.exe


This will run Blender with the Terminal window:



You can create a batch file, this opens up Blender via Command Prompt automatically: 


  A batch file is a kind of script file in DOS, OS/2 and Windows. It consists of a series of commands to be executed by the command line interpreter, stored in a plain text file


blender.bat

"c:\&lt;blender installation directory&gt;\blender.exe"




2. Copy the Output, Errors or Warnings

Switch to the Command Prompt. RMB > Mark to enable text selection, hit Enter to copy:



Alternatively you can  you can also redirect the output to a text file when using the command line: 

c:\&lt;blender installation directory&gt;\blender.exe &gt; %homepath%\mylogfile.txt




Further reading: 


https://en.wikipedia.org/wiki/Command-line_interface
https://www.codecademy.com/articles/command-line-commands